## Syllabus & textbook homework for Math 251:05-10, spring 2006

 This is a very rapid plan of study. A great deal of energy and determination will be needed to keep up with it. Modifications may be necessary. Please send comments to the lecturer. Periodic assignments (Maple labs, workshops, etc.) may be due at times, and additional problems may be suggested. The text is the fifth edition of Stewart's Calculus: Early Transcendentals, Brooks/Cole, 1999, ISBN 0-534-39321-7. A calendar of spring semester dates correlated with the syllabus follows the "plan of study". The calendar may be helpful.

Syllabus and suggested textbook homework problems for 640:251:05-10
LectureTopic(s)Relevant text sectionsSuggested problems
1 R3 and vectors 12.1
12.2
12.1: 3, 4, 7, 8, 23, 26, 27, 29, 32
12.2: 5, 7, 12, 19, 20, 23, 26, 29, 31
2Dot product
Cross product
12.3
12.4
12.3: 1, 3, 7, 11, 15, 20, 24, 27, 36, 37, 41, 42, 45, 51
12.4: 2, 13, 23, 30, 34, 41, 42
3Lines & places 12.5 12.5: 3, 8, 12, 13, 19, 23, 26, 28, 35, 39, 46, 47, 67
4 Vector functions, curves
Derivatives, integrals
13.1
13.2
13.1: 1, 5, 9, 10, 12, 19, 20, 21
13.2: 5, 8, 9, 11, 12, 15, 18, 23, 26, 33, 38, 51
5Arc length; curvature
Motion
13.3
13.4
13.3: 1, 2, 3, 4, 11, 13, 14, 15, 16, 27, 29a, 56a
13.4: 13, 16, 19, 23, 35 (13.4 to Kepler's laws)
6 Several variable functions
Limits; continuity
14.1
14.2
[12.6]
14.1: 29, 41, 43, 53
14.2: 5, 7
[12.6: 4, 7, 13, 27]
7Partial derivatives
Tan. planes, lin. approx.
14.3
14.4
14.3: 14, 15, 17, 21, 26, 36, 47, 48, 67ad
14.4: 16, 17, 32, 37
8 The Chain Rule14.5 14.5: 3, 17, 35, 46
9 Directional derivs
14.6 14.6: 7, 10, 11, 13, 21, 24, 39
10Max/min 14.7 14.7: 2, 3, 5, 7, 8, 12, 14, 27, 28, 36, 43, 47, 48
11 Lagrange multipliers14.8 14.8: 3, 5, 8, 9, 18, 38
12 Exam 1 (timing approximate!)
13 Double & iterated ints 15.1
15.2
15.2: 1, 3, 12, 13, 21
14 More double integrals
& in polar coordinates
15.3
15.4
15.3: 1, 3, 7, 9, 14, 24, 26, 37, 38, 43, 44
15.4: 9, 10, 11, 12
15 Some applications
Changing variables
15.5
15.9
15.5: 3, 7, 12
15.9: 3,11 (15.9 for double integrals)
16 Triple integrals 15.7 15.7: 3,5,9,10,32,36,37
17 Cyl. & sph. coordinates
Triple integrals
12.7
15.8
12.7:35, 37, 39, 43, 55
15.8: 3,5,9,12,18,29,33,35
18 Vector fields
Line integrals
16.1
16.2
16.1: 5, 11, 13, 15, 17
16.2: 9, 12, 13, 16, 31
19 More line integrals
20 FTC for line integrals16.3 16.3: 3, 4, 5, 6, 11, 12, 27, 28
21 Green's Theorem 16.4 16.4: 1, 8, 10, 15
22 Exam 2 (timing approximate!)
23 Curl & divergence 16.5 16.5: 4, 12hijkl, 19, 33
24 Parametric surfaces
Surface area
15.6
16.6
15.6: 4, 9
16.6: 21
25 Surface integrals 16.7 16.7: 5, 14, 19, 24, 41
26 Stokes Theorem 16.8 16.8: 1, 2, 9, 15
27 Divergence Theorem 16.9 16.9: 5, 15, 19
28 Catch-up; a discussion of the {heat|diffusion} equation if there is time & interest.

Important spring semester dates,
with useful (?) references to the lectures
Spring semester begins: Tuesday, January 17
Sunday, January 29, 2006: Chinese New Year (Bing-Xu) [after #4]
Tuesday, January 31, 2006: Islamic New Year 1427 [#5 on this day]
Thursday, February 2, 2006: Groundhog Day [before #6]
Tuesday, February 14, 2006: Valentine's Day [#9 on this day]
Monday, February 20, 2006: President's Day [before #11]
Wednesday, March 1, 2006: Ash Wednesday [after #13]
Spring recess begins: Saturday, March 11 [after #16]
Friday, March 17, 2006: St. Patrick's Day
Spring recess ends: Sunday, March 19
Monday, March 20, 2006: Vernal Equinox 1:25pm (EST) [before #17]
Saturday, April 1, 2006: April Fools' Day [after #20]
Sunday, April 2, 2006: Daylight savings time begins at 2:00 AM
Thursday, April 13, 2006: Passover [before #24]
Friday, April 14, 2006: Good Friday [#24 on this day]
Sunday, April 16, 2006: Easter Sunday
Regular classes end: Monday, May 1 [after #28]
Reading days: Tuesday, May 2; Wednesday, May 3
Spring exams begin: Thursday, May 4
Final exam, sections 05-07: Friday, May 5, 12-3
Final exam, sections 08-10: Wednesday, May 10, 8-11
Spring exams end: Wednesday, May 10